On the holographic origin of the Bekenstein-Hawking entropy of 1/16 BPS AdS_5 black holes

Abstract:

Providing a microscopic derivation of the entropy of supersymmetric asymptotically AdS_5
black holes has been an open problem for 15 years. In the talk I will present progress in this
direction. On the gravity side of the AdS/CFT correspondence, I will describe a BPS limit of
black hole thermodynamics by first focussing on a supersymmetric family of complexified
solutions and then reaching extremality. In this limit the black hole entropy is the Legendre
transform of the on-shell gravitational action with respect to a set of chemical potentials
subject to a specific constraint. The latter follows from supersymmetry and regularity in the
Euclidean bulk geometry. The gravitational analysis instructs us that the dual N=1
superconformal field theory is defined on a twisted S^1 x S^3 with complexified chemical
potentials obeying the constraint, and localization allows to compute the corresponding
partition function exactly. This computation defines a generalization of the supersymmetric
Casimir energy, whose Legendre transform at large N precisely reproduces the Bekenstein-
Hawking entropy of the black hole.

Quantum ergodicity on graphs : from spectral to spatial delocalization

Abstract:

We study the eigenfunctions of discrete Schrödinger operators on finite graphs of large size,
and their (de)localization properties. To measure delocalization, we use a criterion of
"quantum ergodicity" borrowed from the subject of quantum chaos. We can prove
delocalization in this sense for some families of graphs, typically : regular graphs and their
small perturbations. We show that quantum ergodicity is related to ``spectral delocalization'',
namely the fact that the spectrum of the ideal infinite system is absolutely continuous.

Finite-size instabilities are unphysical phase transitions that plague several parameterizations of effective interactions used in self-constistent mean-field calculations. They take the form of large-amplitude oscillations of the isovector density, or the vector (spin) density if time reversal symmetry in not enforced. I will briefly review a study we made concerning the isovector instabilities and discuss a quantitative tool that we have developed in order to detect and avoid them during the fit of the parameters of an interaction. Since the so called bubble (or semi-bubble) nuclei show significant oscillations in proton and neutron densities often quantified by a depletion factor, it is interesting to see how the proximity of an isovector instability may be correlated with this depletion factor. Finally, I will revisit some results for several nuclei considered as having a possible bubble structure and question the predictive power of the zero or finite-range interactions used for these predictions.

Partial compositeness can be used to explain the fermion mass hierarchy and predict the sfermion mass spectrum in a
supersymmetric model. It assumes that the Higgs and third-generation matter superfields are elementary fields, while the first two matter
generations are composite, with a linear mixing between elementary superfields and supersymmetric operators with large anomalous dimensions.
This then gives rise to a split-like supersymmetric model that explains the fermion mass hierarchy while simultaneously predicting an inverted
sfermion mass spectrum with a gravitino LSP that is consistent with LHC and flavor constraints. The model therefore intricately connects the sector
responsible for the generation of flavor with supersymmetry breaking to produce a unique sparticle spectrum.

One of the most puzzling recent experimental discoveries in condensed matter physics has been the observation of quantum oscillations in insulating materials SmB6 and YbB12 [1,2]. Both materials are strongly correlated f electron systems for which a gap develops due to a hybridization between conduction electrons and strongly correlated f electrons, and thus a large resistivity at low temperatures can be measured. Our understanding of quantum oscillations is rooted in the existence of a Fermi surface; electron bands, which form the Fermi surface, form Landau levels in a magnetic field. When the magnetic field strength is changed, the energy of these Landau levels changes which lead to an oscillatory behavior in almost all of the observable properties. However, insulating materials like SmB6 and YbB12 do not possess a Fermi surface, thus there are no electrons, which can form Landau levels, close to the Fermi energy.
On the other hand, SmB6 and YbB12 are both good candidates for topological Kondo insulator. Naturally, the question arises, if these quantum oscillations can be due to the interplay between topology and strong correlations.
We here answer this question by showing results of dynamical mean field theory in a magnetic field for a two dimensional topological Kondo insulator. We demonstrate that the gap closing, described for a noninteracting continuum model with momentum dependent hybridization [3], persists for a topological Kondo insulator on a two dimensional (2D) lattice. Furthermore, we demonstrate that the amplitude of quantum oscillations is strongly enhanced due to correlations, which makes them easily observable in quantities like magnetization and resistivity over a wide range of magnetic fields before the magnetic breakdown occurs.

Bridgeland stability structure/condition on a triangulated category is a vast generalization of the notion of an ample line bunlde (or polarization) in algebraic geometry. The origin of the notion lies in string theory, and is applicable to derived categories of coherent sheaves, quiver representations and Fukaya categories. In a category with Bridgeland stability every objects carries a canonical filtration with semi-stable pieces, an analog of Harder-Narasimhan filtration.
It is expected that for categories over complex numbers Bridgeland stability structures often admit analytic enhancements, similar to the relation between ample bundles and usual Kaehler metrics. In a sense, this should be a generalization Donaldson-Uhlenbeck-Yau theorem which syas that a holomorphic vector bundle over compact Kaehler manifold is polystable if and only if it admits a metrization satisfying hermitean Yang-Mills equation.
In my course I will talk about a non-archimedean analog of analytic Bridgeland stability. I will show several examples, results and conjectures. In particular, I'll introduce non-archimedean moment map equations, generalized honeycomb diagrams, and hypothetical stability on derived categories of coherent sheaves on maximally degenerating varieties over non-archimedean fields.

I will discuss two novel proposals to probe Dark Matter (DM) with existing and upcoming data.
1. Cosmic rays constitute our arguably unique direct access to energy domains of 10 TeV and
above, and a wealth of data is delivered/expected from current/near-future telescopes
(ANTARES, IceCube, KM3NeT, HESSII, CTA, LHAASO, CALET,...). Heavy DM constitutes
therefore an ideal BSM target for these experiments: I will discuss the theory and
phenomenology of DM models that evade challenges like the so-called unitarity bound, and
propose related searches at such telescopes.
2. DM lighter than a GeV is notoriously a challenge for direct detection experiments. I will
propose to rely on the DM component that is unavoidably accelerated by scatterings of cosmic-
rays, that make it possible to detect DM at experiments with large energy thresholds and
volumes, like SuperKamiokande and DUNE. I will derive a new strong limit from public data and
discuss search strategies at current and future neutrino experiments.

In this talk a new production mechanism for vector dark matter (VDM) is presented in which
the VDM is produced at the end of inflation. This mechanism relies on a pseudo scalar
coupling between the inflaton and the vector field strength which leads to a tachyonic
instability and exponential production of one transverse polarization of the vector field,
reaching its maximum near the end of inflation. These polarized transverse vectors can
account for the observed dark matter relic density in the mass range micro-eV to tens of TeV.
Furthermore, since they are produced coherently with very high occupation number and with a
single polarization, the nature of the VDM today is in the form of helical dark matter fields
who's typical size is determined by the Hubble scale at the end of inflation. Some of the
potential phenomenology of these objects is also discussed.

Anisotropic gauge theories: from chiral fermions to new phases of matter

Abstract:

We review the effect of introducing anisotropic couplings for lattice gauge theories and show that these can lead to new, ``layered'', phases, beyond the bulk confining and Coulomb phases, known in abelian gauge theories. The new phases can be interpreted as describing the effects of flux compactifications and generalize the Kaluza-Klein paradigm of extra dimensions. Extra dimensions have been, in fact, used to describe defects in condensed matter systems and anisotropic gauge theories can be also understood as allowing the description of more elaborate defects.
Coupling matter to the gauge fields leads to a consistent, non-perturbative, description of chiral fermions, provided the anomalies are properly cancelled, and can describe edge states and their currents
while scalar fields lead to a quite elaborate phase diagram. The challenges of assembling these ingredients to study supersymmetric theories will be touched on, as a way of describing how such systems can be consistently closed, a la Parisi-Sourlas.

Consider a simplicial complex that allows for an embedding into R^d. How many faces of dimension d/2or higher can it have? How dense can they be? This basic question goes back to Descartes' "Lost Theorem" and Euler's work on polyhedra. Using it and other fundamental combinatorial problems, we introduce a version of the Kähler package beyond positivity, allowing us to prove the hard Lefschetz theorem for toric varieties (and beyond) even when the ample cone is empty. A particular focus lies on replacing the Hodge-Riemann relations by a non-degeneracy relation at torus-invariant subspaces, allowing us to state and prove a generalization of theorems of Hall and Laman in the setting of toric varieties and, more generally, the face rings of Hochster, Reisner and Stanley. This has several applications including full characterization of the possible face numbers of simplicial rational homology spheres, a generalization of the crossing lemma.)

New Planckian quantum phase of the Universe before Inflation: Its present day and Dark Energy implications

Abstract:

The physical history of the Universe is completed by including the quantum planckian and super-planckian phase before Inflation in the Standard Model of the Universe in agreement with observations. In the absence of a complete quantum theory of gravity, we start from quantum physics and its foundational milestone: the universal classical-quantum (or wave-particle) duality, which we extend to gravity and the Planck domain. A new quantum precursor phase of the Universe appears beyond the Planck scale. Relevant cosmological examples as the Cosmic Microwave Background, Inflation and Dark Energy have their precursors in this era. A whole unifying picture for the Universe epochs and their quantum precursors emerges with the cosmological constant as the vacuum energy, entropy and temperature of the Universe, clarifying the so called cosmological constant problem which once more in its rich history needed to be revised. The consequences for the deep universe surveys, and missions like Euclid will be outlined.

The search for cosmic particle accelerators capable of reaching the PeV ($10^{15}$ eV) range, PeVatrons, is a crucial science target of the very-high-energy (gamma-ray domain $\sim$ TeV= $10^{12}$ eV) community. Such accelerators are essential in the context of the problem of the origin of Galactic cosmic rays, and more generally, in order to understand the physical mechanisms involved in the production of PeV particles. Subsequent to the acceleration of PeV particles, the production of gamma rays in the 100 TeV range is expected. Explorations in this energy domain are thus natural in the search for PeVatrons, where gamma—ray instruments are already accumulating data. Relying on Monte Carlo simulations, we explore the capabilities of current instruments to identify the most promising candidates.

Two-loop scattering amplitudes are a vital component in high-precision
cross section calculations at the LHC. At higher multiplicities, the
increased number of scales can make the algebra of analytic amplitude
calculations intractable. In this talk, we discuss how to apply numerical
techniques to sidestep this intermediate complexity and combine them
with physical properties of the amplitude to efficiently determine its
analytic form. In particular we focus on planar five-point amplitudes in
QCD.

Soft gravitational radiation from high energy collisions: a progress report

Abstract:

I will review recent developments on soft gravitational radiation from ultra-relativistic collisions. Calculations based on recent developments in the eikonal approach and in soft-graviton theorems can be successfully compared in their common region of applicability. Combining the results of both approaches leads to a knee in the spectrum at a typical "Hawking frequency” and to a bump at wavelengths comparable to the impact parameter of the collision.

The computation of form factors for the spin chains has always been one of the most important problems of the theory of quantum integrable systems. It gained even more importance when it was shown that the dynamical structure factors can be computed using explicit analytic representations for the form factors and these numerical results give extremely good predictions for neutron scattering experiments. It was also recently demonstrated that the form factor analysis leads to a very powerful method of asymptotic computation of the correlation functions and dynamical structure factors. In this talk I’ll review these recent developments and introduce the lqtest results on the form factors in the thermodynamic limit of the spin chains in zero magnetic field.

Bridgeland stability structure/condition on a triangulated category is a vast generalization of the notion of an ample line bunlde (or polarization) in algebraic geometry. The origin of the notion lies in string theory, and is applicable to derived categories of coherent sheaves, quiver representations and Fukaya categories. In a category with Bridgeland stability every objects carries a canonical filtration with semi-stable pieces, an analog of Harder-Narasimhan filtration.
It is expected that for categories over complex numbers Bridgeland stability structures often admit analytic enhancements, similar to the relation between ample bundles and usual Kaehler metrics. In a sense, this should be a generalization Donaldson-Uhlenbeck-Yau theorem which syas that a holomorphic vector bundle over compact Kaehler manifold is polystable if and only if it admits a metrization satisfying hermitean Yang-Mills equation.
In my course I will talk about a non-archimedean analog of analytic Bridgeland stability. I will show several examples, results and conjectures. In particular, I'll introduce non-archimedean moment map equations, generalized honeycomb diagrams, and hypothetical stability on derived categories of coherent sheaves on maximally degenerating varieties over non-archimedean fields.

The Lifetime Frontier: Search for New Physics with Long-Lived Particles

Abstract:

There is a growing interest in the High Energy community in searching for new physics with
long-lived particles which decay at displaced vertices. Many models exhibit this feature. I will
describe one of such models : the electroweak-scale non-sterile right-handed neutrino model.
In this model, non-sterile right-handed neutrinos as well as other "mirror" quarks and leptons
can be produced at the LHC and their decay products in the form of standard model particles
appear at displaced vertices. A deep connection between the theta-angle of strong CP and
neutrino masses will be presented.

The dimer model is a model from statistical mechanics corresponding to random perfect matchings on graphs. Circle patterns are a class of embeddings of planar graphs such that every face admits a circumcircle. In this talk I describe a correspondence between dimer models on planar bipartite graphs and circle pattern embeddings of these graphs. As special cases of this correspondence we recover the Tutte embeddings for resistor networks and the s-embeddings for Ising models. This correspondence is also the key for studying Miquel dynamics, a discrete integrable system on circle patterns.

Axion–like particles (ALPs) can convert into photons in several different ways: in an external
magnetic field (known as the Primakoff effect), by decay into two photons, or through
parametric amplification of incoming radio photons in an oscillating ALP field within a
narrow frequency range. For non–relativistic ALPs all three effects can give rise to radio
lines, in particular from astrophysical objects with strong magnetic fields or from regions
with ALP over–densities, such as ALP stars. I will give an overview over estimated
intensities and prospects for detectability of such radio lines.

Bridgeland stability structure/condition on a triangulated category is a vast generalization of the notion of an ample line bunlde (or polarization) in algebraic geometry. The origin of the notion lies in string theory, and is applicable to derived categories of coherent sheaves, quiver representations and Fukaya categories. In a category with Bridgeland stability every objects carries a canonical filtration with semi-stable pieces, an analog of Harder-Narasimhan filtration.
It is expected that for categories over complex numbers Bridgeland stability structures often admit analytic enhancements, similar to the relation between ample bundles and usual Kaehler metrics. In a sense, this should be a generalization Donaldson-Uhlenbeck-Yau theorem which syas that a holomorphic vector bundle over compact Kaehler manifold is polystable if and only if it admits a metrization satisfying hermitean Yang-Mills equation.
In my course I will talk about a non-archimedean analog of analytic Bridgeland stability. I will show several examples, results and conjectures. In particular, I'll introduce non-archimedean moment map equations, generalized honeycomb diagrams, and hypothetical stability on derived categories of coherent sheaves on maximally degenerating varieties over non-archimedean fields.